Sudden stratospheric warmings (SSWs) are one of the large uncertainties in climate modelling. Being sensitive to initial conditions, they show large spread between the models. Analysing the causes behind these differences in historical runs could lead us to better understanding of SSWs in future projections. It has been shown that SSWs are heavily connected to the wave forcing, both resolved as well as parameterised. Values of parameterised drag have large spread between the models, mostly due to the different parameterisations and various tuning. This in turn can affect the resolved waves, bringing another uncertainty to the models. For those reasons, wave forcing in models is very important topic of current research.

In this paper the authors analyse historical data from 2 reanalysis and 7 CMIP6 models. They compare both resolved (EPD) and parameterised wave (GWD) drag, taken over locations, which are relevant in the polar vortex during SSW development and in the aftermath. The analysis of resolved waves and residual circulation is done using the classical approach of transformed Eulerian mean (TEM) equations. The authors show how EPD and GWD correlate to changes in time of zonal mean zonal wind and to the advection by the residual circulation. The results nicely demonstrate how each of the wave forcings influences those two variables, differentiating between the stratosphere and mesosphere. The authors also present an inter-event analysis.  The manuscript is well written and comprehensible, bringing valuable insight to SSWs in models, which can point us in the right direction for future research endeavours in this area. I recommend it for publishing with minor comments.

Minor comments:

1. In the abstract on the line 12, the sentence ‘However, the forcing-response relation across events in the stratosphere is similar for each model, but not in the mesosphere.’ can be confusing. Possibly sentence such as ‘Although the forcing-response relation across individual SSW events is similar for each model in the stratosphere, this does not hold in the mesosphere.’ would be clearer?
2. In figure 1 you show calculated SSW frequencies based on criterion by Charleton and Polvani (2007). Do you think other approaches (e.g. vortex moments as in Seviour et al., 2013) would give significantly different values and dates, which could in turn change the analysis of the composites? Since the used criterion uses strictly set thresholds – reversal of the zonal mean zonal winds at 60°N at 10 hPa – it is quite limiting (which is generally true for most of the SSW definitions). It could be interesting to provide second figure with set of frequencies based on another criterion just to illustrate how much the results do/do not depend on the chosen method.
3. On the line 110 you describe how the anomalies are calculated. Could you please specify how the annual cycles were smoothed? Also, did the 30-year mean include the dates where the SSW was happening? If yes, this way the mean values could be influenced enough to result in lesser anomalies in cases of models with high SSW frequencies (especially IPSL-CM6A-LR).

Technical comments

1. In Figure 4, parts of lines which denote significance or difference from ERA5 are too thick to properly distinguish in some places. Especially in plot b), where ERA 5 is then almost invisible. Possibly you could make the lines thinner and at places, where the values are not significant (a) or significantly different from ERA5 (b), you could make the lines dashed?
2. In Figures 7 and 8, some of the coefficients are hard to read. Maybe a table with those coefficients could be provided to summarise the results of these plots?
3. I noticed that in several figures there are values missing for model MIROC6. After looking at figure S6 in the supplement I can see that there are missing values for ADV and EPD near the top of the model. I did not find any reference to this in the text. Could you please provide some information regarding this?
4. On lines 252 and 258 there are two sentences concerning relationship between GWD and EPD which provide similar information I believe.
   • ‘Moreover, there is not linearity in the GWD versus EPD relation (not shown) pointing out that there is not a fixed balance between them.’
   • ‘It should be added that EPD and GWD are not correlated with each other (not shown).’

Comment/question regarding possible extension of the study:

• As you mention in your manuscript, it has been observed, that split SSWs tend to be underestimated in models (Hall et al., 2021), which is connected to geometry of the polar vortex and its strength in the lower stratosphere. Have you considered dividing the data based on the type of SSW before the analysis? It could be interesting to see if the found relationships differ based on the type.

References:

Charlton, A. J., and L. M. Polvani, 2007: A new look at stratospheric sudden warmings. Part I: Climatology and modeling benchmarks. J. Climate, 20, 449–469, doi:10.1175/JCLI3996.1.

Seviour, W. J. M., D. M. Mitchell, and L. J. Gray, 2013: A practical method to identify displaced and split stratospheric polar vortex events. Geophys. Res. Lett., 40, 5268–5273, doi:10.1002/grl.50927

Hall, R. J., Mitchell, D. M., Seviour, W. J., and Wright, C. J.: Persistent model biases in the CMIP6 representation of stratospheric polar vortex variability, Journal of Geophysical Research: Atmospheres, 126, e2021JD034 759, 2021.

I enjoyed reading this manuscript and I would like to thank the authors for performing such an excellent and important study. I believe the manuscript is nearly ready for publication although I did miss some explanations. I hope that adding some explanations for the methodology and perhaps fixing a couple of words will improve the manuscript and make it ready for acceptance. 

Comments:

L42: downward shrink? Maybe downward flow, or subsidence?

L73: What is the period used for the reanalyses?

L88 and Figure 1: can you really statistically distinguish, for example, 0.60 in MRI and 0.62 in MERRA? Can you provide some statistical estimates on the effect of sampling?

Also, the frequency on y-axis is relative with respect to the total number of SSW simulated by particular model, right? Their add up to 1? I would specify this clearly. The alternative is the total fraction per each month, so that they would add up to the total frequency per season.

L103: Sorry for naïve question but why do you attribute the vertical advection to the Coriolis effect? I would not think of w_star*du/dz as of a Coriolis effect.

L119: “different chemical composition” could you clarify this statement? I would naively assume that the altitude must play a role too because the radiative damping should be related to optical depth, which in turn depends on altitude even if the chemical composition were homogenous throughout the atmosphere.

L211-224: I think you need to be explicit about your math. How do you get the 2/3 and 1/3 partitioning? By comparing m1 and m2? Are the values normalized? Please explain it.

L225-227: Related to the previous question – why should m1 and m2 add up to 1?

L252: There is NO linearity…  

L273: The –> the (no need to capitalize)

L276: agreement in what?